I have read all of the posts with regard to the first message. Please, understand that you will not burn in Hell if you don't love this child.
Having said that, please, examine the REASONS (not excuses) that you detest this child. She will, forever, be your husband's child and was part of the package when you married him. You must have spent time with this child before you married your spouse, noting that she had behavioral issues, and chose to expose your own child to her influence, regardless.
Forget the pain and disruption that this kid experiences every time she's shuffled around - you must accept the fact that this kid has learned to behave in this manner as a means of survival. Without a doubt, her behavior is completely inappropriate, but it has been learned. Her demands (and, expectations) of toys, theme parks, food, etc., are an obvious indication that she is attempting to fill an enormous, bottomless emotional void in the ONLY WAY THAT A CHILD KNOWS: with things. If she has a screaming fit, LET HER! Walk away. The more attention that you give to her behavior (good, bad, or seemingly benign), the more she will push the edges of the envelopes! If you refuse to attend to every screaming fit, pout, tantrum, demand, whine, and/or toss of the head, you will provide a positive example of what is acceptable and what is not. Finally, your husband should be the disciplinarian, here, with your support to back him up. He needs to take a 100% proactive role in seeing that this kid gets the help that she needs, and that a clear, CIVIL line of communication exists between himself and his ex FOR THE BENEFIT OF THE CHILD.
There are obviously some serious dynamics going on, here. "Very young" does not answer the age of the child when the separation/divorce began. It does, indeed, have a deep, deep impact upon a child regardless of their age. The relationship between your spouse and the ex sounds acrimonious, at the very least, and THIS can leave a permanent scar on this kid's psyche.
Absolutely, suggest that this child submit to a complete physical. It would also be very wise to have her tested by a child psychologist. MEDICATION IS NOT THE ANSWER, here. Communication between your spouse, his ex, and you is imperative, if any hope of helping this child is to be realized.
You've only been married to this man for less than 2 years - had you ever spoken with his ex-wife on a reasonable basis? Are you aware of the dynamics (BOTH sides, now) of their separation and divorce? How long had you known your husband before you married? There's a lot of information, here, that will have a direct impact upon the dynamics of this whole messy situation, and, trust me: the kid's behavior is just a symptom of the deeper issues that rankle between your husband and his ex.
If it were me, I would seek counseling for myself and my child, observe what steps my spouse took to initiate proper testing and treatment for his daughter, and begin formulating whatever plan might be necessary, from there, with my individual counselor/therapist.
Speaking from personal experience, there is something very wrong, here, and the core of this kid's behavior will, without a doubt, be discovered at the roots of the relationship between your spouse and his ex. And, laying blame or finding fault with this kid's mother is not the answer - again, there are some very serious issues that need to be addressed for the sake of the daughter who had absolutely NO CHOICE as to whom her parents would be, whether or not they would remain married, or whether they would place HER needs before their own.